Effects of geometry and flow rate on secondary flow and the mixing process in static mixers—a numerical study

A method based on computational fluid dynamics (CFD) for the characterization of static mixers using the Z factor, helicity and the rate of striation thinning is presented. These measures were found to be well-suited for the characterization of static mixers as they reflect the pressure drop, the formation of secondary flow, i.e. vortices, and their effect on the mixing process. Two commercial static mixers, the Kenics KM and Lightnin Series 45, have been characterized. In the mixers investigated, secondary flow is formed in the flow at the element intersections and due to the curvature of the mixer elements. The intensity of the vortices is higher in the Lightnin than the Kenics mixer due to edges in the middle of the Lightnin mixer elements. The formation of vortices affects the Z factor by an increase in the power requirement, and the rate of striation thinning by an increase in the stretching of the striations. The formation of vortices was observed at a Reynolds number of 10 in both mixers with aspect ratios of 1.5. However, the intensity of the vortices was greater in the Lightnin than the Kenics mixer, which was observed in not only the magnitude of the helicity, but also the Z factor, rate of striation thinning and the distribution of striation thickness.The distribution in striation thickness is shifted towards thin striations as the flow rate is increased from below to above the Reynolds numbers of which vortices were first observed, but some striations still pass the mixer elements almost unaffected, which can be seen in the skewness of the distribution of the striation thickness, which shifts from being negative to positive.     

Performance of Kenics static mixer over a wide range of Reynolds number

The present study deals with the numerical simulation of flow patterns and mixing behaviour in Kenics static mixer over a wide range of Reynolds number. Three different sets of Kenics mixer (aspect ratio = 1.5) comprised of 3, 9 and 25 elements each have been characterized. The Reynolds number was varied in the range of 1 to 25,000 (i.e., from laminar to turbulent flow regime). The numerical approach takes into account the aspects of the fluid flow at higher Reynolds number values including circumferential velocity profiles at different cross-sections within the Kenics mixer, which were neglected in previous studies. It was observed that cross-sectional mixing in the turbulent flow regime takes place up to 30% of each element length at element-to-element transition; beyond that velocity profiles were uniform. The experiments were also carried out to measure the circumferential and axial velocity profiles and pressure drop in three different Kenics Mixers using air as fluid. The pressure drop per unit element (ΔP/η) was found to be independent of the number of Kenics mixing elements used in the system. The total pressure drop across Kenics mixer obtained by CFD simulations were compared with the experimental pressure drop values and correlations available in the literature. The numerical results were found in good agreement with the experimental as well as the results reported in the literature. A new pressure drop correlation in the Kenics static mixer has been developed.     

Quantification of laminar mixing in the kenics static mixer: An experimental study

The laminar flow field in a Kenics KM static mixer has been studied using laser induced fluorescence and digital image analysis. Mixing was quantified by measurement of the number average striation thickness, variance of striation widths and interfacial area, for elements of length to diameter (L/D) ratios of 0.8, 1.0, 1.5 with 90° twist per element. From flow visualisations, transitions were observed in the flow where vortices developed above the first and second elements at Reynolds numbers of 43 and 90 for L/D = 0.8 and Reynolds numbers of 55 and 105 for L/D = 1.0. It was found that these vortices did not appreciably enhance mixing based on striation thickness and variance of striation widths measurements after 4 to 5 elements. The influence of viscosity ratio showed a viscosity ratio (dyed stream/bulk stream) of I had faster interfacial area growth and created more uniform mixtures compared to a viscosity ratio of 0.2 for flow rate ratio of 0.2.     

Residence time distributions of power law fluids in motionless mixers

Motionless mixers, which are also known as static mixers, can often be modeled as open, circular tubes with parabolic velocity distributions except at a few isolated planes where radial mixing occurs via an instantaneous coordinate transformation. The extension of this idea to the processing of non-Newtonian fluids is straightforward. The parabolic velocity distribution is replaced by whatever fully developed velocity profile is appropriate for the fluid. Experimental confirmation is given for the flow of carboxymethylcellulose solutions through motionless mixers of the Kenics variety. A previous observation that four Kenics elements are equivalent to one plane of complete radial mixing holds for these power law fluids as well as for Newtonian fluids.     

Gas/liquid dispersions with a SMX static mixer in the laminar regime

A Sulzer SMX mixer was used to disperse gas into viscous, Newtonian and non-Newtonian fluids. The investigation covered the effect of the dispersed phase volume fraction, the viscosity of the continuous phase, the mixer length and the power draw. The flow regime was kept laminar in all the experiments. The dispersion of gas was carried out with gas concentrations between 1% and 7% in volume. Using the “process viscosity” concept, it was possible to collapse all the measured sizes on a single master curve by using the energy consumption in the mixer as the common variable between the experiments. Comparison was made with a Kenics mixer. The SMX mixer was found to be better adapted to the dispersion task due to its internal structure.     

LAMINAR FLOW HEAT TRANSFER WITH INLINE MIXERS INSERTS

Heat transfer coefficients were measured for heat transfer to a Newtonian fluid flowing in laminar flow through a tube with inline mixer inserts. Kenics “Static” mixer and Ross LPD mixer inserts were studied as heat transfer augmentation devices. The mixer inserts were in the inner tube of a concentric tube heat exchanger. Steam was condensed in the annulus of the exchanger. Significant heat transfer enhancement was obtained with both inserts at the expense of even greater pressure drop increases. The use of the Ross mixer insert gave greater augmentation than did the use of the kenics insert. An analysis using the analogy between momentum and heat transfer allowed the prediction of heat transfer coefficients from pressure drop measurements. The predicted coefficients were in good agreement with experimentally measured heat transfer coefficients for laminar flow.     

Experimental investigation of the flow dynamics of rheologically complex fluids in a Maxblend impeller system using PIV

The Maxblend^® mixer is used in processes involving Newtonian, shear-thinning or viscoelastic fluids and, as for many impellers, little is known regarding the relationship between the rheological behavior and the flow and mixing properties. An experimental study of the hydrodynamics in the Maxblend was carried out using Newtonian and non-Newtonian fluids in laminar and early transitional regimes. Flow fields were measured by two-dimensional particle image velocimetry (PIV) to evaluate the effect of highly shear-thinning and viscoelastic behavior on the performance of the mixer. The experimental setup consisted of a 35-L tank equipped with two baffles. A total of 100 measurements were proven to be sufficient in order to attain convergence of the velocity components for all studied regimes. Isolated zones in the highly shear-thinning case were observed by means of a decolorization technique. Elasticity in the laminar regime produced a reversal of the flow and a solid body rotation in the bottom region of the tank. Fluid velocity magnitude and spread were observed to be reduced by the presence of elastic forces.     

Reactions and residence time distributions in motionless mixers

Motionless mixers are modeled as open, circular tubes with parabolic velocity distributions except at a few isolated planes where radial mixing occurs via an instantaneous coordinate transformation. Possible transformations are constrained by continuity of volumetric flow. Complete flow inversion appears the theoretically optimal transformation, being superior to complete mixing. A model consisting of intermediate planes of complete mixing approximates existing experimental data on the Kenics Static Mixer when four Kenics elements are made equivalent to a single plane of complete mixing. This model preserves the essential nature of a laminar flow residence time distribution while providing a relatively simple means of estimating mixer performance.     

LAMINAR FLOW HEAT TRANSFER WITH INLINE MIXERS INSERTS

Heat transfer coefficients were measured for heat transfer to a Newtonian fluid flowing in laminar flow through a tube with inline mixer inserts. Kenics “Static” mixer and Ross LPD mixer inserts were studied as heat transfer augmentation devices. The mixer inserts were in the inner tube of a concentric tube heat exchanger. Steam was condensed in the annulus of the exchanger. Significant heat transfer enhancement was obtained with both inserts at the expense of even greater pressure drop increases. The use of the Ross mixer insert gave greater augmentation than did the use of the kenics insert. An analysis using the analogy between momentum and heat transfer allowed the prediction of heat transfer coefficients from pressure drop measurements. The predicted coefficients were in good agreement with experimentally measured heat transfer coefficients for laminar flow.     

Numerical investigation of blade shape in static mixing

The mixing performance of the KMX and SMX static mixers have been compared using 3D high-resolution computational fluid dynamics (CFD) simulations. Although these mixers have a similar design composed of layers of blades, their blade shape is different: curved for the KMX and flat for the SMX. The flow of a Newtonian fluid in steady laminar regime has been considered as the benchmark of the study. The simulation was first validated by assessing the pressure drop vs. the number of mixer elements and the results were found to be in good agreement with experimental data. To evaluate the mixing quality, cross-section stream function, extensional efficiency, mean shear rate, residence time, intensity of segregation, stretching, and Lyapunov exponent have been selected. Analysis of the flow pattern and mixing parameters shows differences between the mixers and it appears that the curved blade is more efficient than the flat blade design at the expense of a slightly higher pressure drop. In practice, the KMX mixer should provide a higher mixing rate at high viscosity ratio than the SMX mixer. © 2004 American Institute of Chemical Engineers AIChE J, 51: 44–58, 2005     

数值模拟静态混合器结构对PS/CO_2熔体温度的影响

利用专用CFD软件Polyflow对SMX型和Kenics型静态混合器中PS/CO_2发泡溶液进行数值模拟计算,分析比较不同板厚在不同元件个数条件下两种静态混合器消耗的压力损失,以及不同CO_2浓度对静态混合器压力损失的影响;并引入"离散系数"分析比较两种静态混合器出口温度均匀性的变化.数值模拟的结果表明:SMX型静态混合器冷却效果优于Kenics型静态混合器,并且SMX型静态混合器出口温度均匀性高于Kenics型静态混合器.     

Laminar mixing of shear thinning fluids in a SMX static mixer

Flow and mixing of power-law fluids in a standard SMX static mixer were simulated using computational fluid dynamics (CFD). Results showed that shear thinning reduces the ratio of pressure drop in the static mixer to pressure drop in empty tube as compared to Newtonian fluids. The correlations for pressure drop and friction factor were obtained at Re_MR?100. The friction factor is a function of both Reynolds number and power-law index. A proper apparent strain rate, area-weighted average strain rate on the solid surface in mixing section, was proposed to calculate pressure drop for a non-Newtonian fluid. Particle tracking showed that shear thinning fluids exhibit better mixing quality, lower pressure drop and higher mixing efficiency as compared to a Newtonian fluid in the SMX static mixer.     

Kenics混合器混合性能的模拟研究

利用Fluent有限元分析软件计算了流体流过Kenics混合器过程中的应变速率,进而分析混合元件转速与旋转式Kenics混合器混合效率的关系,以及混合元件与机筒间隙对静态和旋转式Kenics混合器对混合效率的影响。模拟分析结果表明:旋转式Kenics混合器混合效率随转速增加而提高;减小混合元件与机筒间间隙有利于增加静态Kenics混合器混合效率,但间隙的减小对旋转式Kenics混合器混合效率的影响却很小。     

Numerical investigation of the mixing efficiency of the Ekato Paravisc impeller

The viscous mixing characteristics of the Ekato Paravisc are compared with those of an anchor and a double helical ribbon. The methodology is based on 3D CFD finite element-based simulations. The predictions are first validated by comparing the Newtonian and non-Newtonian power consumptions and mixing times against literature experimental data. Then, the computed 3D laminar flow patterns and several mixing performance criteria (power consumption, pumping capability, intensity of segregation, mixing time, mixing efficiency and specific energy) of the impellers are investigated. It is shown that the Paravisc mixer characteristics lie between that of the other impellers at low Reynolds number.     

Use of an areal distribution of mixing intensity to describe blending of non‐newtonian fluids in a kenics KM static mixer using PLIF

The performance of KM static mixers has been assessed for the blending of Newtonian and time‐independent non‐Newtonian fluids using planar laser induced fluorescence (PLIF). A stream of dye is injected at the mixer inlet and the distribution of dye at the mixer outlet is analyzed from images obtained across the pipe cross section. The effect of number of mixing elements, fluid rheology, and apparent viscosity ratio for two‐fluid blending have been investigated at constant mixture superficial velocity of 0.3 m s^?1. Aqueous solutions of glycerol and Carbopol 940 are used as the working fluids, the latter possessing Herschel–Bulkley rheology. The PLIF images have been analyzed to determine log variance and maximum striation thickness to represent the intensity and scale of segregation, respectively. Conflicting trends are revealed in the experiments, leading to the development of an areal‐based distribution of mixing intensity. For two‐fluid blending, the addition of a high viscosity stream into the lower viscosity main flow causes very poor mixing performance, with unmixed spots of this component observable in the PLIF image. © 2013 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 60: 332–342, 2014     

Resistance properties of coal-water paste flowing in pipes

On the basis of analyzing the mechanism of coal-water paste (CWP) slip flow, the similitude criterion, known as general Reynolds number Re_g which can characterize the state of non-Newtonian fluid flow in pipes, was put forward. The energy loss coefficient of CWP laminar flow has the same form as Newtonian fluid, i.e. λ=64/Re_g. Re_g holds good not only for the slip flow of non-Newtonian fluid, but also for slip-free flow as a steady-state laminar flow in pipes. The results obtained from experiments show that the energy loss coefficient of CWP laminar flow in pipes has the same form as Newtonian fluid.     

Kenics型静态混合器内分散相液滴破碎和聚结过程的CFD-PBM数值模拟

采用CFD-PBM耦合方法对Kenics型静态混合器内分散相油滴破碎及聚并行为进行数值模拟研究,分析了雷诺数、混合元件数、元件长径比等参数对分散相液滴粒径的影响,揭示了分散相在Kenics静态混合器内流动过程中液滴粒径的演化规律。结果表明,随雷诺数增大,分散相液滴出口粒径不断减小,并出现临界趋势;静态混合器的前几个元件段粒径下降较快,雷诺数越高,油滴破碎达到稳定粒径所需的流动距离越短,而元件数仅在较低雷诺数下对粒径有明显影响;相同雷诺数下元件的长径比越小,其出口粒径越小,且达到稳定所需流动距离越短。     

Mathematical modelling of hydrothermal performance for Kenics type static mixer using power law obeying fluids

In this study, analytical, numerical, and experimental works are presented to demonstrate hydrothermal characteristics of a flow choosing non-Newtonian behaviour through a Kenics type static mixer. Experiments are conducted by varying the superficial fluid velocities of the heterogeneous mixture oil with Sudan dye and water, as well as for the homogeneous aqueous system, consisting of CMC (2 wt%) in water. Six static mixing elements are placed in series, and the corresponding wall temperatures of the inline pipe are varied over a range of 293–363 K. In the context of hydrodynamic study, analytical models are solved using the Bessel function and Laguerre function and validated with the in-house experimental results and numerical results. In the thermal performance study, mathematical models are formulated based on differential transformation method (DTM) and homotopy perturbation method (HPM), and have been validated with the numerical results. The deviation among the experimentally measured average pressure drops estimated from our experiment and that predicted by analytical models is found to be as low as ±8.1%. The deviation between the analytical results obtained from the HPM and DTM method and numerical results based on the finite volume method solution of the same equation is observed as low as ±4%. Additionally, both proposed analytical methods used are compared with each other to evaluate the dimensionless swirl flow velocity and temperature gradient of the inline Kenics Static mixer. In the thermal performance study, we observe that the DTM is in good agreement with the numerical method as compared to HPM.     

Kenics静态混合器在水平液固循环流化床中的研究

为了解决水平液固循环流化床中颗粒分布不均匀问题,在内径29 mm、长4 m的水平有机玻璃管流化床内放入Kenics静态混合器,采用CCD图像测量与数据处理系统考察静态混合器的结构、个数、安装位置对液固二相流中颗粒分布的影响;同时,利用U型管压差计考察不同条件下静态混合器的压降。实验结果表明:Kenics静态混合器能明显地改善管内颗粒分布情况;单个扭率Y=3.5的Kenics静态混合器压降最小;2个扭率Y=3.5的Kenics静态混合器间距为40 mm时对颗粒分布影响长度是最长的。